The likelihood is that both the writer and the original readers of the Apokalypsis [Apocalypse] to which you are referring, typically, would have conceived of the Abyss, or "the bottomless pit" (as the ESV has it), as being under the ground/earth.
The view of the world as a binary cosmos composed of two ontologically different existences termed as matter (“physical” things) and non-matter (“spiritual” things) is by and large a by-product of Greek philosophy popularised by Platon [Plato]. This view is especially problematic when considering the original meaning of the word physical, which is simply “natural,” from physis, “nature”; and the original meaning of the word spiritual, which literally is “having to do with [the breeze/puff of a] breath.” [So technically anything that exists—even a spirit—is physical, i.e. it has a nature.]
For most ancient peoples, the physis or nature of “spirits” was that they were quite undoubtedly creatures of this world, who often dwelt in the air or in the literal sky, which would make sense of them being “breezes.” Like ordinary air, breath or wind, “spirits” were invisible but nonetheless tangible. (See Ephesians 2.2 regarding “the prince of the authority of the air”.) Life too was described as a phenomenon of people having “spirit,” i.e. air/breath moving around in their bodies, coursing through their veins. (Cf. how God puffs a breeze of his breath/“spirit” through the nostrils of the first human clay protoplast to vivify it in Genesis 2.7.) Death was the result of this air-flow ceasing, at which point, the breath/spirit had exited the body and floated up into the atmosphere or sunk beneath the ground (see Ecclesiastes 3.21 & 12.7).
Similarly most of these ancient peoples conceived of a relatively small, self-contained, geocentric universe. Whatever was divine was enthroned above the sky or the heavens, while the dead dwelt literally under the earth, hence the generic translation “Underworld” for the abode of the departed in many cosmologies that have survived from long ago.
In the cosmology of the ancient Western Semites, among whom were the Hebrews as well as certain “ethnic groups” or “nations” classified as Canaanites and Phoenicians, the Abyss would have been the deepest part of the cosmos, the lowest stratum of the universe beneath both the land and the sea, and below even the realm of Sheol (called Hades by the Greeks and frequently translated into English using the Anglo-Saxon word “Hell”), the home of the dead, itself. This parallels quite neatly with Ancient Greek cosmology in which the Abyss is called Tartaros [Latinised as Tartarus] and is, according to mythographers like Hesiod, as far away from the floor of Hades as the sky is from the earth’s surface. Or in other words it is a sort of upside-down sky.
For Ancient Near Easterners, like the Hebrews, the Egyptians and the Syrian Canaanites, the sea represented the edge of death, chaos and the waters of darkness out of which the universe first arose. Upon venturing deep or far enough into the sea one would be bound to encounter gigantic sea monsters (such as the one that swallowed the Hebrew prophet Jonah; and see also Amos 9:3b), the dwellings of the dead (down to which Jonah says he was dragged by the monster), and also destructive, malevolent beings who signified the forces of disorder in nature as well as in human society.
These murky and unfathomable depths—the unknown and the fear with which that comes—are what the Abyss refers to. The word abyss itself means “unfathomable,” or more literally “depth-less,” in the sense of “so deep that it’s practically meaningless to say that it consists of depths at all.” (In case that concept sounds somewhat nonsensical it might help to think of it in the same terms as the sky, which, for cultures the world over, has always baffled people in terms of how to describe its limits, or the lack thereof. In modern Western cultures this unfathomable quality is referred to by the virtually inane term “space.”)
Joseph Henry Thayer’s Greek-English Lexicon of the New Testament uses a Latin term for the location of the Abyss, saying that it is in Orcus, which is a Roman equivalent of Hades. In Thayer’s definition, which would appear to be describing the universe as it was understood by the ancients, the Abyss is “a very deep gulf or chasm in the lowest parts of the earth” which was used to house all of the dead but it was also in particular “the abode of demons”.
John Jeffrey Dodson’s lexicon agrees with Thayer’s regarding this. As far as “demons” or “evil spirits” abiding in the abyss is concerned, Thayer and Dodson both seem to be arriving at this conclusion from the story of the “Legion” demoniac(s) at Gerasa/Gadara whose story is told in Matthew 8, Mark 5 and Luke 8. In this episode, one or two men is/are infested with daimonēs which escape from the man/men, go into a nearby herd of pigs, and summarily send the livestock over the cliff to their death in the water body below. Matthew and Mark call the water body “the sea” while Luke calls it a lake, which is apparently what the daimonēs in his account refer to as “the abyss” (v. 31). (On all accounts what is in view in this scene is Lake Gennesaret/Galilee/Tiberias, also called the Sea of Tiberias or of Galilee.)
This connection between salt-waters and the abyss, in this passing mention of Luke, corroborates something that Paul does with the same word in Romans 10.7 when he describes Christ as being fetched up out of the abyss, in reference to his return from the nekrōn [dead ones] after his demise. Here Paul is quoting Deuteronomy 30.13, where Moses says to Israel that the directive [mitzvah] which he is issuing him is neither hidden nor distant. “It is not beyond the sea, that you should say, ‘Who will pass through the sea on our behalf and bring it to us, that we might recognise and adhere to it?’ For the Word is intimate with you, in your mouth and in your heart, that you may adhere to it.” Moses’ intent here is almost certainly to remind Israel of the manner in which, forty years earlier, they had crossed the sea, which was a perilous place to be in the conception of the Israelites as well as in the worldview of the Egyptians from whom they were fleeing.
In Romans, Paul takes this a lot deeper in forming the analogy between the sea and the netherworld. If the nekrōn, out of whom Christ is to be fetched up, are located in the Abyss, the implication is that the Abyss is either the abode of the dead (as asserted by Thayer’s, Dodson’s and other lexicons) or at least a “place” through which they somehow pass at some point. Another saying of Paul would further augment the link between the sea and the Abyss (whatever the Abyss actually is) on the one hand and Sheol/Hades/Hell on the other. In Acts 13.35 Paul quotes Psalm 16.10 as though it is Jesus Christ who is speaking in the passage, saying that YHWH will not abandon his nephesh [i.e. self/ life/ personality] in Sheol, commonly translated as “You will not leave my soul in Hell.”
